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Mixtures of discrete decomposable graphical models

Yulia Alexandr, Jane Ivy Coons and Nils Sturma
Vol. 15 (2024), No. 2, 269–293
DOI: 10.2140/astat.2024.15.269
Abstract

We study mixtures of decomposable graphical models, focusing on their ideals and dimensions. For mixtures of clique stars, we characterize the ideals in terms of ideals of mixtures of independence models. We also give a recursive formula for their ML degrees. Finally, we prove that second secant varieties of all other decomposable graphical models have the expected dimension.

Keywords
graphical models, secant varieties, decomposable graphs, dimension, identifiability, clique sums, maximum likelihood estimation, expected dimension, ideals of secant varieties
Mathematical Subject Classification
Primary: 05C50, 14Q15, 62H30, 62R01
Milestones
Received: 15 February 2024
Revised: 21 May 2024
Accepted: 3 June 2024
Published: 3 December 2024
Authors
Yulia Alexandr
University of California
Los Angeles, CA
United States
Jane Ivy Coons
St John’s College
University of Oxford
Oxford
United Kingdom
Nils Sturma
Technical University of Munich
Garching
Germany
© 2024 MSP (Mathematical Sciences Publishers).